{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Statistics Made Simple\n",
    "\n",
    "Code and exercises from my workshop on Bayesian statistics in Python.\n",
    "\n",
    "Copyright 2019 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If we're running on Colab, install empiricaldist\n",
    "# https://pypi.org/project/empiricaldist/\n",
    "\n",
    "import sys\n",
    "IN_COLAB = 'google.colab' in sys.modules\n",
    "\n",
    "if IN_COLAB:\n",
    "    !pip install empiricaldist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "sns.set_context('talk')\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from empiricaldist import Pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The World Cup problem\n",
    "\n",
    "In the 2018 FIFA World Cup final, France defeated Croatia 4 goals to 2.  Based on this outcome, we can answer the following questions:\n",
    "\n",
    "1. How confident should we be that France is the better team?\n",
    "\n",
    "2. If the same teams played again, what is the chance Croatia would win?\n",
    "\n",
    "To answer these questions, we have to make some modeling assumptions:\n",
    "\n",
    "1. Goal scoring can be well modeled by a Poisson process, so the distribution of goals scored by each team against the other is Poisson($\\lambda$), where $\\lambda$ is a goal-scoring rate, measured in goals per game.\n",
    "\n",
    "2. For two random World Cup teams, the distribution of goal scoring rates is Gamma($\\alpha$), where $\\alpha$ is a parameter we can choose based on past results.\n",
    "\n",
    "To determine $\\alpha$, I used [data from previous World Cups](https://www.statista.com/statistics/269031/goals-scored-per-game-at-the-fifa-world-cup-since-1930/) to estimate that the average goal scoring rate is about 1.4 goals per game.\n",
    "\n",
    "We can use `scipy.stats.gamma` to compute the PDF of the Gamma distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import gamma\n",
    "\n",
    "α = 1.4\n",
    "qs = np.linspace(0, 6)\n",
    "ps = gamma(α).pdf(qs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use `qs` and `ps` to make a `Pmf` that represents the prior distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3870150350170796"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior = Pmf(ps, index=qs)\n",
    "prior.normalize()\n",
    "prior.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decorate_rate(title):\n",
    "    \"\"\"Labels the axes.\n",
    "    \n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plt.xlabel('Goal scoring rate')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior.plot()\n",
    "decorate_rate('Prior distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This prior implies:\n",
    "\n",
    "1. The most common goal-scoring rates are near 1.\n",
    "\n",
    "2. The goal-scoring rate is never 0; eventually, any team will score against any other.\n",
    "\n",
    "3. The goal-scoring rate is unlikely to be greater than 4, and never greater than 6."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The likelihood function\n",
    "\n",
    "Suppose you are given the goal-scoring rate, $\\lambda$, and asked to compute the probability of scoring a number of goals, $k$.  The answer is given by the Poisson PMF:\n",
    "\n",
    "$ \\mathrm{PMF}(k; \\lambda) = \\frac{\\lambda^k \\exp(-\\lambda)}{k!} $\n",
    "\n",
    "**Exercise 1:** Write a likelihood function that takes $k$ and $\\lambda$ as parameters `data` and `hypo`, and computes $\\mathrm{PMF}(k; \\lambda)$.\n",
    "\n",
    "You can use NumPy/SciPy functions or `scipy.stats.poisson`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood(data, hypo):\n",
    "    \"\"\"Likelihood function for World Cup\n",
    "    \n",
    "    data: integer number of goals in a game\n",
    "    hypo: goal scoring rate in goals per game\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    # TODO: fill this in!\n",
    "    return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from math import factorial\n",
    "\n",
    "def likelihood(data, hypo):\n",
    "    \"\"\"Likelihood function for World Cup\n",
    "    \n",
    "    data: integer number of goals in a game\n",
    "    hypo: goal scoring rate in goals per game\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    k = data\n",
    "    λ = hypo\n",
    "    return λ**k * np.exp(-λ) / factorial(k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from scipy.stats import poisson\n",
    "\n",
    "def likelihood(data, hypo):\n",
    "    \"\"\"Likelihood function for World Cup\n",
    "    \n",
    "    data: integer number of goals in a game\n",
    "    hypo: goal scoring rate in goals per game\n",
    "    \n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    k = data\n",
    "    λ = hypo\n",
    "    return poisson.pmf(k, λ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Update\n",
    "\n",
    "First we'll compute the posterior distribution for France, having seen them score 4 goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.656282076744656"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "france = Pmf(prior, copy=True)\n",
    "\n",
    "france.update(likelihood, 4)\n",
    "france.plot(label='France')\n",
    "decorate_rate('Posterior distribution, 4 goals')\n",
    "\n",
    "france.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2:** Do the same for Croatia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.695567117265963"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Solution\n",
    "\n",
    "croatia = Pmf(prior, copy=True)\n",
    "\n",
    "croatia.update(likelihood, 2)\n",
    "croatia.plot(label='Croatia', color='C3')\n",
    "decorate_rate('Posterior distribution, 2 goals')\n",
    "\n",
    "croatia.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of superiority\n",
    "\n",
    "Now that we have a posterior distribution for each team, we can answer the first question: How confident should we be that France is the better team?\n",
    "\n",
    "In the model, \"better\" means having a higher goal-scoring rate against the opponent.  We can use the posterior distributions to compute the \"probability of superiority\", which is the probability that a random value drawn from France's distribution exceeds a value drawn from Croatia's.\n",
    "\n",
    "Remember that `Pmf` provides `choice`, which returns a random sample as a NumPy array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.7176326530612243"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_france = france.choice(size=1000)\n",
    "sample_france.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 3:** Generate a similar sample for Croatia; then compute the fraction of samples where the goal-scoring rate is higher for Croatia.  \n",
    "\n",
    "Hint: use `np.mean`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7011836734693875"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "sample_croatia = croatia.choice(size=1000)\n",
    "sample_croatia.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.755"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(sample_france > sample_croatia)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the basis of one game, we have only moderate confidence that France is actually the better team."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting the rematch\n",
    "\n",
    "Now we can take on the second question: If the same teams played again, what is the chance Croatia would win?\n",
    "\n",
    "To answer this question, we'll generate a sample from the \"posterior predictive distribution\", which is the number of goals we expect a team to score.\n",
    "\n",
    "If we knew the goal scoring rate, $\\lambda$, the distribution of goals would be $Poisson(\\lambda)$.\n",
    "\n",
    "Since we don't know $\\lambda$, we can use the sample we generated in the previous section to generate a sample of goals, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "goals_france = np.random.poisson(sample_france)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def decorate_goals(title):\n",
    "    \"\"\"Labels the axes.\n",
    "    \n",
    "    title: string\n",
    "    \"\"\"\n",
    "    plt.xlabel('Goals scored')\n",
    "    plt.ylabel('PMF')\n",
    "    plt.ylim([0, 0.32])\n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.78"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_france = Pmf.from_seq(goals_france)\n",
    "pmf_france.bar(label='France')\n",
    "decorate_goals('Predictive distribution')\n",
    "plt.legend()\n",
    "\n",
    "goals_france.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This distribution represents two sources of uncertainty: we don't know the actual value of $\\lambda$, and even if we did, we would not know the number of goals in the next game."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4:** Generate and plot the predictive distribution for Croatia."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.711"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "goals_croatia = np.random.poisson(sample_croatia)\n",
    "\n",
    "pmf_croatia = Pmf.from_seq(goals_croatia)\n",
    "pmf_croatia.bar(label='Croatia', color='C3')\n",
    "decorate_goals('Predictive distribution')\n",
    "plt.legend()\n",
    "\n",
    "goals_croatia.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a sense, these distributions represent the outcomes of 1000 simulated games."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 5:** Compute the fraction of simulated rematches Croatia would win, how many France would win, and how many would end in a tie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(goals_croatia > goals_france)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.563"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(goals_france > goals_croatia)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.167"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "np.mean(goals_france == goals_croatia)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming that Croatia wins half of the ties, their chance of winning the rematch is about 33%."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
